# Limit rational function without L'H

1. Mar 15, 2013

### whatlifeforme

1. The problem statement, all variables and given/known data
evaluate.

2. Relevant equations
$lim_{x->0+} \frac{\sqrt{x}}{\sqrt{sinx}}$

3. The attempt at a solution
i've tried l'hopital's and it is just endless cycle.

2. Mar 15, 2013

### Dick

It's the same as sqrt(x/sin(x)). You know the limit of x/sin(x), right?

3. Mar 15, 2013

### Staff: Mentor

Sometimes, L'Hopital's Rule is not the way to go. Under the right conditions, you can switch the order of the limit operation and the function in the limit.
$\lim f(g(x)) = f(\lim g(x))$

Also, as long as all quantities are positive,
$$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$$

4. Mar 15, 2013

### whatlifeforme

yes, but it is of the form 0/0.

5. Mar 15, 2013

### Dick

That doesn't mean you HAVE to use l'Hopital. You know the limit of x/sin(x), use l'Hopital on that. Then take the square root. Use that the square root is continuous for positive arguments.